#3 should be piK, pi/2 + 2piK since sin=0 or 1
#4. should be 0° and 30° since they asked for principal values
1,2,5,6 look good
7-10 I'll have to check later, or another expert can come by.
1. Which expression is equivalent to cos 2theta for all values of theta ?
cos^2 theta – sin^2 theta ~
cos^2 theta – 1
1 – 2 sin^2 theta
2 sin theta cos theta
2. Use a half–angle identity to find the exact value of sin 105°.
-1/2(sqrt)(2 + Sqrt3)
1/2(sqrt)(2 + Sqrt3) ~
1/2(sqrt)(2 + Sqrt2)
11/2(sqrt)(1 + Sqrt3)
3.) Solve cos x tan x - sin^2x = 0 for all real values of x.
piK, pi/2 + 2piK
pi/2 + piK, 2pik
pi/2 + 2piK, 3pi/2 + 2piK
piK, pi/4 +2piK ~
4.) Solve 2 sin2x – sin x = 0 for principal values of x.
60° and 120°
0° and 150° ~
0° and 30°
60°
5.) Solve csc x + 2 = 0 for 0 < x < 2pi.
pi/6 and 5pi/6
pi/6 and 7pi/6
4pi/3 and 5pi/3
7pi/6 and 11pi/6 ~
6.) Solve 2 cos x – 1 = 0 for 0 <x< 2.
pi/6 and 5pi/6
pi/3 and 5pi/3 ~
pi/3 and 2pi/3
7pi/6 and 11pi/6
7.) Write the equation 3x + 4y – 7 = 0 in normal form.
3/5x + 4/5y + 7/5 = 0
-3/5x - 4/5y - 7/5 = 0
-3/5x - 4/5y + 7/5 = 0 ~
3/5x + 4/5y - 7/5 = 0
8.)Write the standard form of the equation of a line for which the length of the normal is 4 and the normal makes an angle of 45° with the positive x–axis.
sqrt2x + sqrt2y +8 = 0
2x + 2y – 8 = 0
sqrt2x + sqrt2y -8 = 0 ~
2x + 2y + 8 = 0
9.) Write the standard form of the equation of a line for which the length of the normal is 3 and the normal makes an angle of 135° with the positive x–axis.
sqrt2^x – sqrt2y + 6 = 0 ~
sqrt2^x + sqrt2y - 6 = 0
sqrt2^x – sqrt2y - 6 = 0
sqrt2^x + sqrt2y + 6 = 0
10.) Find the distance between P (–2, 1) and the line with equation x – 2y + 4 = 0.
4sqrt5/5
0 ~
-4sqrt5/5
5/4
the ones with~ are my answers
1 answer